On the complexity of blocks-world planning

Abstract

In this paper, we show that in the best-known version of the blocks world (and several related versions), planning is difficult, in the sense that finding an optimal plan is NP-hard. However, the NP-hardness is not due to deleted-condition interactions, but instead due to a situation which we call a deadlock. For problems that do not contain deadlocks, there is a simple hill-climbing strategy that can easily find an optimal plan, regardless of whether or not the problem contains any deleted-condition interactions. The above result is rather surprising, since one of the primary roles of the blocks world in the planning literature has been to provide examples of deleted-condition interactions such as creative destruction and Sussman's anomaly. However, we can explain why deadlocks are hard to handle in terms of a domain-independent goal interaction which we call an enabling-condition interaction, in which an action invoked to achieve one goal has a side-effect of making it easier to achieve other goals. If different actions have different useful side-effects, then it can be difficult to determine which set of actions will produce the best plan.